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2016 Explicit rank bounds for cyclic covers
Jason DeBlois
Algebr. Geom. Topol. 16(3): 1343-1371 (2016). DOI: 10.2140/agt.2016.16.1343

Abstract

For a closed, orientable hyperbolic 3–manifold M and an onto homomorphism ϕ: π1(M) that is not induced by a fibration M S1, we bound the ranks of the subgroups ϕ1(n) for n , below, linearly in n. The key new ingredient is the following result: if M is a closed, orientable hyperbolic 3–manifold and S is a connected, two-sided incompressible surface of genus g that is not a fiber or semifiber, then a reduced homotopy in (M,S) has length at most 14g 12.

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Jason DeBlois. "Explicit rank bounds for cyclic covers." Algebr. Geom. Topol. 16 (3) 1343 - 1371, 2016. https://doi.org/10.2140/agt.2016.16.1343

Information

Received: 4 November 2013; Revised: 19 October 2015; Accepted: 4 November 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1354.57008
MathSciNet: MR3523041
Digital Object Identifier: 10.2140/agt.2016.16.1343

Subjects:
Primary: 20F05 , 57M10
Secondary: 20E06

Keywords: JSJ decomposition , ‎rank‎ , rank gradient

Rights: Copyright © 2016 Mathematical Sciences Publishers

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